For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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What's probability of THREE rolls in 5 dice (yahtzee) to get specific combinations:

What's probability of THREE rolls in 5 dice (yahtzee) to get these combinations: 1-1: You get at least two “1” dice in 5 dice when rolling. 1-1-1: You get at least three “1” dice in 5 dice when ...
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1answer
35 views

Roll Dice- Expected Winnings [on hold]

I have a problem like this: At a charity game you pay \$1 to roll a die. If you roll a 6, you get \$5. Otherwise, you get nothing. How do I set up a probability distribution and what is the ...
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2answers
24 views

Probability of 3 dices

Been looking through past exam papers and came across this question: Three fair dices are rolled. The probability that all three dices show 5 is 1/216. Is this true?
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1answer
41 views

Best strategy for rolling 20-sided and 10-sided dices

There are a 20-sided (face value of 1-20) dice and a 10-sided (face value of 1-10) dice. A and B respectively roll the 20 and 10-sided dices. Both of them can roll the dice twice. They may choose ...
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1answer
35 views

D6 Event Tree Probability Question. [closed]

One has tried looking this one up and Googling it, One is also dispraxic so while math can be tricky if one can get the concept and explanation behind something generally work at it until one ...
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1answer
45 views

Roll 2 dice adding and rolling one die, probability of being equal

Roll two dice, add the results, call the number x. Roll one die call that number y. What is the probability that x and y are equal? Help please.
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1answer
30 views

How many times to roll a die before getting $n$ consecutive sixes given $m$ occurences?

Given a unbiased dice how to find the average number of rolls required to get $n$ consecutive sixes given already $m$ number of sixes occurred where $m\leq n$. I know how to solve using n consecutive ...
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2answers
61 views

Number of dice rolls taken to reach a certain sum

I was reading about sums of dice rolls and Chernoff bounds, and I thought of a question I couldn't obviously answer with the techniques I know. You're given some number $x$ and told it was generated ...
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1answer
43 views

Probablility of a Dice Game

Player A rolls $m$ dice, while Player B rolls $m + 1$ dice. If Player A rolls $a$ $n$'s and Player B rolls $b$ $n$'s, then Player A wins if $a > b$ . Otherwise, Player A rolls up to $k$ of the $m$ ...
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1answer
22 views

Changing Faces of Six-sided Die to replicate the probabilities of a normal pair?

So, in my computer science class, we are given this problem here: Is it possible to modify the faces on a pair of conventional six-sided dice so as to exactly replicate the probabilities of a ...
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3answers
65 views

Die roll, value of 4 must follow value of 1 to win

I came across a "die roll" probability question that has me stumped. Two fair die are being rolled by players A and B, who alternate, with A rolling first (ie. A then B then A then B...so long as the ...
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1answer
30 views

Whats the probability of rolling factors of 2?

You roll 1 die. what is the probability of rolling factors of $2$ with it?
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1answer
45 views

Finding the coefficient of a generating function

Given $f(x) = x^4\left(\frac{1-x^6}{1-x}\right)^4 = (x+x^2+x^3+x^4+x^5+x^6)^4$. This is the generating function $f(x)$ of $a_n$, which is the number of ways to get $n$ as the sum of the upper faces of ...
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1answer
33 views

Probability Dice Game Question

I have the following problem to solve that deals with probability (something I haven't done since Grade 8 (6 years ago)) This is a one player game and it is described for $q$ sided dice. You start by ...
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1answer
18 views

Calculating probability of a dice with different numbers [duplicate]

I was given a problem in class: ...
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1answer
32 views

Probabilities of rolling a fair die twice?

a) One of the dice is a 4 b) Sum of the dice equals 4 c) Neither dice is a 4 I get really confused with these exercises (I don't know why)
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1answer
18 views

Probability of occurrence vs. Probability of x successes

I've been reading for two hours and I'm having a hard time getting the grasp of these two concepts. I'm developing a tool for a game, in which I'm given n dice and a success threshold (ie. roll at ...
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1answer
56 views

Probability of a tetrahedron (die with 4 faces)?

I have been doing some questions from an exam review with no solution and I have no idea how to work this problem. I know that $Pr(A_1) = \frac{1}{2}$, $Pr(A_2) = \frac{1}{2}$, $Pr(A_3) = ...
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1answer
23 views

$95$ percent confidence interval for roll of two dice

Given a roll of two fair six-sided dice, we know the expectation for a specific result (e.g. a $4$ and another $4$) is $\frac{1}{36}$. But with what certainty could you expect that result in $N$ ...
3
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1answer
78 views

Expected duration of a die game

In a 2 person game, the player who first obtains a $6$ wins. I'm trying to determine the expected number of die rolls needed before a winner is determined. (One turn consists of two die rolls, ...
2
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2answers
61 views

Probability of always rolling 6 on a dice

Suppose I roll a six-sided die $10$ times and each time it shows a $6$. What is the probability of the next roll coming up $6$? You might say $1/6$. But it was never declared to be a fair die. In ...
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2answers
35 views

Consider throwing two six-sided dice. Let X be the sum of the two values and let Y be the product of the two values.

What is the value of $P(X = i, Y = j)$ for $i = 1,2,\cdots,12$ and $j = 1,2,\cdots,36$. Trying to figure out if there is a easier way to figure this out rather than writing out all the values.
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2answers
42 views

Consider throwing two six-sided dice.

Let X be the sum of the two values and let Y be the product of the two values. What is the value of P(Y = i) for i = 1,2,3...36. I am having trouble approaching this problem. We are learning about ...
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4answers
57 views

2 player dice game probability

For some homework in one of my classes, we are given this problem: In a certain dice game, player $A$ rolls six six-sided dice vs. player $B$ who rolls nine four-sided dice. Each player rolls ...
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0answers
18 views

Roll a die until the nth time T that a certain number shows up.

So if we are asked to roll a fair die until the nth time T that a certain number shows up, what would be the probability distribution of T? Example: Roll a fair die until a six shows up three times ...
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2answers
115 views

Rolling two dice 10 times, what is the probability of getting all possible “doubles”?

Rolling two dice 10 times, what is the probability of getting all possibble "doubles": (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) among our rolls? For instance, ...
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1answer
68 views

Dice Math, odds and probability

DISCLAIMER: This will be done with fake money for education purposes. I'm working on a Dice simulation site for a school project, where you play the house and you as a player have to get a higher ...
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2answers
100 views

Toss a die until SIX appears. E (number of ONEs | at leat one TWO) =?

A fair die is tossed repeatedly until a Six appears. Let $X$ denote the number of One's that are thrown in this game/experiment. Let $A$ denote the event that at least one Two was thrown. Compute$ E(X ...
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2answers
25 views

When the game is fair

One player throws dice twice. If he has 2 x 6 on the dice he is receving 8*a. If he has one 6 he will collect 4*a. Otherwise (when he has no 6 at all) he is paying a. For which value of a game is ...
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2answers
57 views

What is the theoretical expected value of the sum of the highest 3 values of 4 fair dice?

Many have estimated the expected value of the common "4d6, drop lowest" roll or averaged a complete enumeration of the possible outcomes. I would like to know the theoretical expression of this value, ...
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2answers
71 views

Is there a way to simulate any $n$-sided die using a fixed set of die types for all $n$?

I am assuming that we can increase the number of dice based on $n$, but they have to be $k$-sided, $k\ge3$. When I say die types, I mean that we are allowed to use non-standard dice such as ...
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3answers
82 views

Probability Questions! [duplicate]

Alex, Bret, and Chloe repeatedly take turns tossing a fair die. Alex begins; Bret always follows Alex; Chloe always follows Bret; Alex always follows Chloe, and so on. Find the probability that Chloe ...
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3answers
68 views

Probability Dice Game Follow Up

Original Question: Paul, Dave and Sarah are rolling a fair six sided die. Paul will go first, always followed by Dave, who is always followed by Sarah, who is always followed by Paul, and so on... ...
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1answer
41 views

probability fair dice question [closed]

a game is played by rolling a fair die repeatedly until the number 2,4, and 6 is obtained. What is the probability that the game ends with 6?
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1answer
16 views

What is the expectation of the first time dice-rolls Z and Z+1 are similar?

We roll a dice. Let $Z=$ the first time the rolls $Z$ and $Z+1$ are similar. What is $E[Z]$ ? What is $E[Z^2]$ ? The problem sounds unnatural to me because i'm asked about a roll $(Z+1)$ that ...
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1answer
34 views

Deciding to place a bet on outcome of a dice roll based on the probability

I have encountered several question of the following format. I have no trouble answering the first half but second half I have no clue on how to proceed. a: If you roll 5 standard six-sided dice, ...
3
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1answer
61 views

What is the expected number of k-length streaks in n rolls?

Given $n$ flips of a coin with success probability $p$, what is the expected number of $k$-length win streaks in $n$? (I've looked for this question online, but the answers always restrict $n$ to be ...
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2answers
76 views

DICE - Rolling at least *k* on *n* six-sided dice - with a twist!

I am putting together a table of dice probabilities for a project I am working on and have found myself intimidated by a little "special case" I'm trying to work with. For determining the probability ...
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1answer
73 views

Game Dice Probability

In the realm of statistical analysis I'm about as green as they come, so forgive me if my question isn't stated perfectly, I'm trying my best to explain. There's a table-top game my friends and I play ...
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3answers
50 views

Dice problem with a stopping rule [closed]

The problem is the following: You roll a die. You get a dollar if the result is 1, 2, 3 and you roll again. If the result is 4 or 5, the game stops and you get the money up to now. If the result is ...
2
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3answers
47 views

Probability Dice Game

Paul, Dave and Sarah are rolling a fair six sided die. Paul will go first, always followed by Dave, who is always followed by Sarah, who is always followed by Paul, and so on... What is the ...
5
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2answers
231 views

Roll a die, pick that many balls from an urn

An urn has $5$ white and $10$ black balls. A die is rolled, and that many balls is drawn from the >urn. What is the probability that all the balls drawn are white? My thinking is that each die ...
4
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1answer
84 views

What is a good strategy for this dice game? [duplicate]

I learned the following dice game from another forum. It was not solved there. The dice game is as follows. You start tossing six dice. After each toss you must put aside at least one of the dice ...
4
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3answers
77 views

Probability of rolling a “1” on a die conditioned on when all rolls are different.

So I have this problem: I am rolling a six sided die 3 times. Conditioned on the rolls all being different, what's the probability at least one die is a "1" So I worked it out like this: ...
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3answers
65 views

A dynamic dice game

I learned the following dice game from another forum. It was not solved there. The dice game is as follows. Toss 6 dice. Each toss you can keep one or more up to the total number of dice tossed. You ...
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2answers
36 views

What is the probability there are a higher total of red “5’s and 6’s” than white “5’s and 6’s”?

You have 3 red 6-sided dice and 3 white 6-sided dice. When you throw the dice, what is the probability there are a higher total of red “5’s and 6’s” than white “5’s and 6’s”? Note: When any 6-sided ...
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1answer
44 views

rolling a seven when at least one die is a four?

I have been working on some stuff like this and I am fairly confused, I wrote some code to see how it works when simulated and I am further from an answer. ...
4
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1answer
88 views

Expected sum of all the n-sided dice rolls until we get n

So the problem is the following. We have an $n$-sided die. We throw it until we get $n$. What's n, if the expected sum of all the throws including the $n$ one is $21$. Now, I did manage to solve it ...
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1answer
36 views

Probability number comes up before another

In craps, say I roll a 5 for the place bet. What is the probability that I roll another 5 before rolling a 7? Is this correct?: $P(5 \text{ before 7}) = P(5) + P(\neg 7 \neg 5, 5) + P(\neg 7 \neg 5, ...
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0answers
62 views

Dice roll game fair price

You and I each roll 1 die each at the same time. I win if I roll a six on one roll, and then a five on the next. You win if you roll two sixes in a row. Who would you bet your money on? Note that You: ...